Case (i) x = npi , cosnpi = 1 or -1 , and sinnpi = 0. But (cos npi)/(sin npi) is indeterminate . So at x= npi , cotnpi is indeterminate. So at x= npi , Lt (cot npi)/npi is also indeterminate and does not exist . Both right limit and left limit are also indeterminates. So at x = npi , Lt n--> infinity (cot npi)/(npi) does ot exist.